Foundation June 2024 Paper 1 Q28
28 Solve \(\quad x + 11 \leqslant 5 - \dfrac{1}{2}x\) (3)
| Answer | Mark | Mark scheme |
|---|---|---|
| \(x \leqslant -4\) | M1 | for a correct first step working with an equation or inequality eg \(x + 11 - 11 \leqslant 5 - \frac{1}{2}x - 11\) or \(x + 11 + \frac{1}{2}x \leqslant 5 - \frac{1}{2}x + \frac{1}{2}x\) or \(2 \times x + 2 \times 11 \leqslant 2 \times 5 - 2 \times \frac{1}{2}x\) |
| M1 | for a full method to solve the inequality or for a critical value of \(-4\) | |
| A1 | for \(x \leqslant -4\) oe as final answer |
Additional guidance
Can work with an equation or incorrect inequality symbol for both M marks
Allow for subtracting 5 from both sides or subtracting \(x\) from both sides.
For M marks step must be carried out not just intention shown.
For example, if you see\[\begin{array}{ccc} x + 11 & \leqslant & 5 - \frac{1}{2}x \\ -11 & & -11 \end{array}\]Award M1 for:\[x \leqslant k - \frac{1}{2}x\]with \(k \ne 5,\ k \ne 16\)
or indicating \(+\frac{1}{2}x\) reaching\[kx + 11 \quad \leqslant \quad 5\]with \(k \ne \frac{1}{2},\ k \ne 1\)
or indicating multiplying by 2 obtaining an equation or inequality with three of four terms correct and no term unchanged.
Award 2 marks for answer of \(x\,?\,-4\) where ? is an = or any incorrect inequality symbol, or for answer shown as just \(-4\)